Simplify the following expression: $ n = \dfrac{9}{4} + \dfrac{-5r}{5r + 7} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{5r + 7}{5r + 7}$ $ \dfrac{9}{4} \times \dfrac{5r + 7}{5r + 7} = \dfrac{45r + 63}{20r + 28} $ Multiply the second expression by $\dfrac{4}{4}$ $ \dfrac{-5r}{5r + 7} \times \dfrac{4}{4} = \dfrac{-20r}{20r + 28} $ Therefore $ n = \dfrac{45r + 63}{20r + 28} + \dfrac{-20r}{20r + 28} $ Now the expressions have the same denominator we can simply add the numerators: $n = \dfrac{45r + 63 - 20r}{20r + 28} $ $n = \dfrac{25r + 63}{20r + 28}$